Equivalent-time sampling systems are used to characterize and display high-speed data signals. An equivalent-time sampling system disclosed by Agoston in U.S. Pat. No. 4,812,769 relies on a trigger signal that is synchronous with the data signal to provide trigger events used for acquiring samples of the data signal. The timing of the acquired samples is progressively varied relative to the trigger events until the number of samples is sufficient to reconstruct the waveform of the data signal on a display. However, a synchronous trigger signal may not be available in optical fiber networks or other communication networks, making it difficult to characterize high-speed data signals within these networks using this type of equivalent-time sampling system. In U.S. Pat. No. 4,678,345, Agoston discloses an equivalent-time pseudorandom sampling system that does not rely on a synchronous trigger signal. Trigger events in this system are provided by the data signal. Time intervals between the trigger events on the data signal establish the relative timing of acquired samples. It is difficult to isolate characteristics of the data signal such as jitter or other timing instabilities using this type of sampling system since timing of sample acquisitions is derived directly from the data signal itself. For example, jitter in the data signal may be masked or enhanced by the equivalent-time pseudorandom sampling system, depending on how the system processes the trigger events. Accordingly, there is a need for a sampling system capable of characterizing a high-speed data signal that does not rely on a synchronous trigger signal and that does not derive the timing of sample acquisitions directly from the data signal.